As explained in my said earlier patents, limitations in prior art laser beam interferometry measurements and in similar prior optical scanning techniques led to the development of the oscillating sensing probes between which and grating or other surfaces, sensing fields were established, as described particularly in my said earlier U.S. Pat. Nos. 5,589,686 and 5,744,799. These scanning sensors relied upon the generation of sinusoidal output voltages, measured after passing through the surface from the  oscillation-controlled probe. By comparison of the phase and amplitude of the oscillation-controlling and resulting sinusoidal output voltages, the development on a continual basis of positional signals indicative of the position of the probe along the surface relative to an adjacent apex of undulations therein, was enabled.
As detailed in said patents, real-time continual nanometer scale position measurement data of the location of a sensing probe relatively moving with respect to an undulating surface stage (an atomic surface or a grating or the like) is achieved through rapid oscillating of the probe under the control of sinusoidal voltages as a sensing field established between the surface and the probe, producing output sinusoidal voltages by the current generated in the sensing field. As therein detailed, signal-processing comparison of the phase and amplitude of such output voltages provides positional signals indicative of the direction and distance off the apex of the nearest atom or undulation of the surface. Circuits for developing such positional signals are disclosed in said patents and, where desired, feedback is effected of the positional signals to control the relative movement of the probe and surface.
There were, however, circumstances where it became desirable to use probing by energy beams, such as by laser beams and other energy beams, as distinguished from physical probe sensors such as capacitor or magnetic probes illustrated in said patents; and, indeed, to use the beam energy not only in probing over the surface, but also as a contributor to the setting up of the sensing energy field with the atomic grating or other surface itself. 
The following sinusoidally phase modulated signal formed as a result of scanning the beam over the grating surface was disclosed in Equation (1) in my U.S. Pat. No. 5,744,799 as,
                                                        p              =                            ⁢                              A                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                                  (                                                            r                      ⁢                                                                                          ⁢                                              ω                        ′                                            ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      ω                      ⁢                                                                                          ⁢                      t                                        +                                                                  ω                        ′                                            ⁢                                              X                        0                                                                              )                                                                                                        =                            ⁢                                                                    AJ                    0                                    ⁢                                                                          ⁢                                      cos                    ⁡                                          (                                                                        ω                          ′                                                ⁢                                                  X                          0                                                                    )                                                                      -                                  2                  ⁢                  A                  ⁢                                                                          ⁢                                      sin                    ⁡                                          (                                                                        ω                          ′                                                ⁢                                                  X                          0                                                                    )                                                        ⁢                                      ∑                                                                  J                                                                              2                            ⁢                            m                                                    -                          1                                                                    ⁢                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              m                                                        -                            1                                                    )                                                                    ⁢                      ω                      ⁢                                                                                          ⁢                      t                                                                      +                                                                                                      ⁢                                                2                  ⁢                  A                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                                      (                                                                  ω                        ′                                            ⁢                                              X                        0                                                              )                                    ⁢                                      ∑                                                                  J                                                  2                          ⁢                          m                                                                    ⁢                      cos                      ⁢                                                                                          ⁢                      2                      ⁢                      m                      ⁢                                                                                          ⁢                      ω                      ⁢                                                                                          ⁢                      t                                                                      ,                                                                        (        1        )            where r is a grating or fringe pattern or probe oscillation amplitude; ω is an angular velocity of the fringe or probe oscillation; X0 is the object position or distance to be measured, ω′ is a spatial frequency of the grating or fringe pattern, A is the amplitude of the modulated current, and J2m, J2m−1 represent the Bessel function of the first kind.
A similar form of equation, however, can be derived for many applications, such as detection of fringe position in Michelson interferometer and absorption stabilized laser wavelength control (D P Blair and P H Sydenham, Phase sensitive detection as a means to recover signals buried in noise, J. Phys. E: Scientific Instruments 1975 Vol. 8, 621-7), where the amplitude sin(ω′X0) and cos(ω′X0) of corresponding harmonic signals are detected as a result of multiplying the output signals by a reference signal with the same frequency of the base harmonic signal and filtering the resultant product through a low pass filter. In this case, the results can be used to control the actuator position X0 at a constant position by keeping such amplitude value constant.
These methods, however, suffer from very slow detection speed since they have to rely on low pass filtering in order to eliminate high frequency noise for the amplitude detection. They also require the arctangent function in order to obtain the value of X0 over one fringe distance with good linearity by utilizing both sin(ω′X0) and cos(ω′X0)  values. This slows the calculation process, and, in addition, also introduces the issues of limited resolution, accuracy and noise immunity, which limit practical use as, for example, a position encoder or similar device.
The techniques of my said earlier patents also teach how to convert the above-described sinusoidal phase modulated signal problem into a rather simple phase modulated signal problem so that many conventional approaches can be readily available in order to extract the position information.
While hereinafter explained in more full detail, my prior patent U.S. Pat. No. 6,639,686 further teaches a more general signal processing position calculation that was found to be particularly useful, involving multiplying the output voltage Vout from the scanning probe, by the second and third order harmonic frequencies of the probe oscillation frequency, with information on an “estimated position” {circumflex over (X)}o included in their phases. As a result, the same position measurement result became obtainable without requiring the controlling of the probe oscillation amplitude at any specific value, thus obviating the need for attendant extra circuits therefor. Equation (22) of this patent readily presented the error signal between the real position Xo of the probe and the estimated position {circumflex over (X)}o such that, by forming a closed loop, such error signal was kept at or near zero, resulting in accurate position information being obtained at Xo={circumflex over (X)}o.
While constituting a significant advance, however, this specific signal processing technique has now been found, in experimental practice, still to suffer from several further earlier-referenced limitations that particularly occur (1) as greater subnanometer precision is sought, (2) higher stage scanner movement speeds are attempted, and (3) simultaneous high accuracy and top speed measuring capabilities are desired. 
It has now fortuitously been discovered, both mathematically and by experimental verification, that the above-described signal processing techniques of my earlier U.S. Pat. No. 6,639,686 can be immeasurably improved by a novel, unexpected, and deliberate use of many harmonic signals in the signal processing, (not just limited to the second and third) and further by elimination of the DC component resulting from initial signal processing multiplication and the substituting therefore of a variety of the harmonic frequencies for the amplitude detection purposes. With these signal processing changes, indeed, all of the prior limitations are surprisingly significantly reduced—(1) obviating non-linear error sensitivity of position measurement due to minute error in probe oscillation amplitude measurement; (2) maintaining position measurement occurring at high stage movement speeds; and (3) achieving simultaneously both high accuracy and top speed measuring capability.
It is to this substantially improved signal processing technique and its significant improved results, accordingly, that the present invention is therefore primarily directed.